Name: ideal gas heat capacity differences
Uploaded: 2023-04-30T12:32:12.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

new-york-state-science-learning-standards

New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

Heat Capacities of an Ideal Gas II

서로 다른 열역학적 과정을 거칠 수 있는 서로 다른 온도에서 이상 기체로 채워진 두 개의 동일한 플라스크를 생각해 보십시오.
일정한 부피 공정에서 첫 번째 플라스크의 가스 온도가 두 번째 플라스크의 온도와 동일하게 증가한다고 가정합니다.
그러면 내부 에너지는 열 변화와 동일하며 몰 열 용량으로 쓸 수 있습니다.
일정한 압력 공정에서 온도가 동일한 양만큼 증가하면 시스템의 내부 에너지가 일부 작업이 수행됨에 따라 변경됩니다.
내부 에너지는 상태 함수이므로 시스템의 내부 에너지 변화는 두 과정에서 동일합니다.
차동 형태의 이상 기체 방정식을 사용하면 수행된 작업을 온도 변화 측면에서 작성할 수 있습니다.
양쪽의 공통 요인을 상쇄함으로써 두 프로세스에 대한 몰 열 용량 간의 관계를 얻습니다.
여기서 R은 보편적인 기체 상수이므로 일정 압력 공정에서 이상 기체의 몰 열 용량은 항상 일정 부피 공정에서 보다 큽니다.

<ol>
	<li>Young, H.D 및 Freedman, RA (2012). 현대 물리학을 가진 대학 물리학. 샌프란시스코, 캘리포니아 : Pearson.637-638.</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전]. 원본 주소 <a href="https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas">https://openstax.org/books/university-physics-volume-2/pages/3-5-heat-capacities-of-an-ideal-gas</a></li>
</ol>

이상기체의 열용량 ii

일정한 부피 조건에서 열역학적 과정을 거치는 시스템의 경우 흡수된 열은 시스템의 내부 에너지를 증가시키는 데에만 사용되며 어떤 종류의 작업에도 사용되지 않습니다. 일정한 압력 조건에서 열역학적 과정을 거치는 시스템의 경우 흡수된 열의 양은 내부 에너지(온도의 함수로)를 증가시키는 것뿐만 아니라 일부 작업을 수행하는 데에도 사용됩니다. 몰열용량은 기체 1몰의 온도를 1단위 높이는 데 필요한 열량입니다. 흡수된 일부 열은 일을 하는 데 사용되므로 온도가 1 단위 증가하려면 일정한 압력을 받는 시스템에 더 많은 열을 추가해야 합니다. 일정한 압력 공정의 몰 열용량은 항상 일정한 부피의 몰 열용량보다 큽니다. 결과적으로, 열역학 제1법칙에 기초한 유도로부터 우리는 다음과 같은 관계를 얻습니다. 즉

<img alt="Equation1" src="/files/ftp_upload/13685/13685_Equation_1.svg" style="text-align: center; height: 18px;" />

따라서 두 몰 열용량의 차이는 상수이며 보편적인 기체 상수인 R과 같습니다. 이상기체상수 또는 몰기체상수라고도 한다. 그 값은 약 8.314이며 몰 비열 용량 J/mol⋅K와 동일한 SI 단위로 표시됩니다. 예를 들어, He의 경우 Cp 및 CV 에 대한 측정값은 20.78 J/mol·입니다. ;K 및 12.47 J/mol·K 입니다. 이것의 차이점은   8.31 J/mol·K는 R에 가깝습니다.

이상기체의 열용량 II

일정한 부피 조건에서 열역학적 과정을 거치는 시스템의 경우, 흡수 된 열은 시스템의 내부를 증가시키기 위해서만 사용됩니다 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

The First Law of Thermodynamics

열역학 제1법칙

KEY TERMS AND CONCEPTS

주요 용어 및 개념

ideal gas heat capacity differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case.

At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at constant pressure than at constant volume.

From the first law of thermodynamics, the two molar heat capacities are related by a simple equation. The difference between the constant-pressure heat capacity, Cp, and the constant-volume heat capacity, Cv, is a constant. That constant is the universal gas constant, R, also called the ideal gas constant or molar gas constant.

The value of R is about 8.314 and it uses the same SI unit as molar specific heat capacity, J/mol·K. A helium example shows this relationship clearly. For He, Cp is 20.78 J/mol·K and Cv is 12.47 J/mol·K. Their difference is 8.31 J/mol·K, which is close to R.

Ideal Gas Heat Capacity Differences

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heat capacities of an ideal gas iii

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Ideal Gas Heat Capacity Differences

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